In a previous paper (Harden et al. in Behav Gen 37:273-283, 2007) models of genotype-environment interaction were fitted to data from the National Merit Twin Study, resulting in evidence for an interaction: the heritability of National Merit Qualifying Test scores increased at higher levels of family income. The present paper investigates two assumptions made in the previous modeling. These were a lack of resemblance between parents for cognitive skill, and possible correlations between family income and a child's genes because of the contribution of parental genes to both. The assumptions were found not to seriously affect estimates of the interaction effect-heritability still increased with income-but they did make a difference for other parameter estimates from the modeling. One possible explanation of the observed interaction, decreasing levels of assortative mating at higher income levels, was examined and found not to be consistent with other evidence from the study. Another possible explanation, a greater freedom of members of DZ pairs at higher income levels to follow independent interests, remained plausible.